Index: Tsagris 2018 - Dirichlet Regression with Zeros

Tsagris 2018 - Dirichlet Regression with Zeros

Routing Summary

Captures Tsagris and Stewart (2018), A Dirichlet Regression Model for Compositional Data with Zeros (arXiv 1410.5011v6): mean-precision Dirichlet regression, zero-adjusted Dirichlet regression (ZADR), four data examples, a simulation study, and limitations. 4 notes plus overview. Motivating PyMC example: E70.

• Need the one-page summary and source map? → Tsagris 2018 - Dirichlet Regression with Zeros - Overview
• Need Dirichlet regression formulas, link, log-likelihood, variable precision? → Tsagris 2018 - Dirichlet Regression with Zeros - Dirichlet Regression
• Need the zero-pattern mixture, selection matrices, ZADR likelihood, algorithm? → Tsagris 2018 - Dirichlet Regression with Zeros - Zero Adjusted Dirichlet Regression
• Need the Florida / glass / foraminifera / Arctic lake tables and simulation? → Tsagris 2018 - Dirichlet Regression with Zeros - Examples and Simulation Results
• Need limitations and comparison with Bear-Billheimer, Scealy-Welsh? → Tsagris 2018 - Dirichlet Regression with Zeros - Discussion and Alternatives

Concept Map

Concept	Note	Type	Depends On	Key Result
Dirichlet mean-precision	Tsagris 2018 - Dirichlet Regression with Zeros - Dirichlet Regression	definition	-	${\alpha }_i=\varphi a_i^{\ast }$
Multinomial-logit link	Tsagris 2018 - Dirichlet Regression with Zeros - Dirichlet Regression	definition	Dirichlet	$d(p+1)+1$ parameters
Zero-pattern mixture	Tsagris 2018 - Dirichlet Regression with Zeros - Zero Adjusted Dirichlet Regression	definition	Dirichlet regression	${\hat{\theta }}_b=n_b/n$
Simple ZADR / ZADR	Tsagris 2018 - Dirichlet Regression with Zeros - Zero Adjusted Dirichlet Regression	theorem	zero-pattern mixture	shared $\beta ,\varphi$ via $Q_b$
Empirical comparison	Tsagris 2018 - Dirichlet Regression with Zeros - Examples and Simulation Results	example	ZADR	foraminifera KL 3.126 vs 3.556
Limitations	Tsagris 2018 - Dirichlet Regression with Zeros - Discussion and Alternatives	concept	all	negative correlations only

Notes

• Tsagris 2018 - Dirichlet Regression with Zeros - Overview — CONTAINS: question, contribution, source map, E70 link.
• Tsagris 2018 - Dirichlet Regression with Zeros - Dirichlet Regression — CONTAINS: Defs. mean-precision Dirichlet, logit link, varying precision; Thm. log-likelihood.
• Tsagris 2018 - Dirichlet Regression with Zeros - Zero Adjusted Dirichlet Regression — CONTAINS: Defs. zero mixture, ZADR; Thm. full likelihood; 4-step algorithm; Python.
• Tsagris 2018 - Dirichlet Regression with Zeros - Examples and Simulation Results — CONTAINS: Tables 1-6, Florida, glass, foraminifera, Arctic lake, simulation design and results, Python.
• Tsagris 2018 - Dirichlet Regression with Zeros - Discussion and Alternatives — CONTAINS: common-parameter assumption, Dirichlet limitations, comparison of alternatives.

Sources

• Tsagris 2018 - Dirichlet Regression Model for Compositional Data with Zeros — Tsagris M, Stewart C (2018), arXiv:1410.5011v6, 18 pp.

See Also

• Greenacre 2023 - Aitchison CoDA 40 Years On - Overview, Generalized Linear Models